Publications

2007

• A mathematical model for the Fermi weak interactions
  
  • Amour Laurent
  • Grébert Benoît
  • Guillot Jean-Claude
  Cubo, a Mathematical Journal, Temuco Departamento de Matemática y Estadística, Facultad de Ciencias e Ingeniería, Universidad de La Frontera, 2007, 9, pp.37-57. We consider a mathematical model of the Fermi theory of weak interactions as patterned according to the well-known current-current coupling of quantum electrodynamics. We focuss on the example of the decay of the muons into electrons, positrons and neutrinos but other examples are considered in the same way. We prove that the Hamiltonian describing this model has a ground state in the fermionic Fock space for a sufficiently small coupling constant. Furthermore we determine the absolutely continuous spectrum of the Hamiltonian and by commutator estimates we prove that the spectrum is absolutely continuous away from a small neighborhood of the thresholds of the free Hamiltonian. For all these results we do not use any infrared cutoff or infrared regularization even if fermions with zero mass are involved.
• A strictly hyperbolic equilibrium phase transition model
  
  • Allaire Grégoire
  • Faccanoni Gloria
  • Kokh Samuel
  Comptes Rendus de l'Academie des Sciences. Série IV, Physique, Astronomie, Elsevier, 2007, 344, pp.135-140. This Note is concerned with the strict hyperbolicity of the compressible Euler equations equipped with an equation of state that describes the thermodynamical equilibrium between the liquid phase and the vapor phase of a uid. The proof is valid for a very wide class of uids. The argument only relies on smoothness assumptions and on the classical thermodynamical stability assumptions, that requires a de nite negative Hessian matrix for each phase entropy as a function of the speci c volume and internal energy. (10.1016/j.crma.2006.11.008)
  DOI : 10.1016/j.crma.2006.11.008
• Using switching detection and variational equations for the shooting method
  
  • Martinon Pierre
  • Gergaud Joseph
  Optimal Control Applications and Methods, Wiley, 2007, 28 (2), pp.95-116. We study in this paper the resolution by single shooting of an optimal control problem with a bang-bang control involving a large number of commutations. We focus on the handling of these commutations regarding the precise computation of the shooting function and its Jacobian. We first observe the impact of a switching detection algorithm on the shooting method results. Then, we study the computation of the Jacobian of the shooting function, by comparing classical finite differences to a formulation using the variational equations. We consider as an application a low thrust orbital transfer with payload maximization. This kind of problem presents a discontinuous optimal control, and involves up to 1800 commutations for the lowest thrust. Copyright c 2000 John Wiley & Sons, Ltd.
• Global weak solutions to a ferrofluid flow model
  
  • Amirat Youcef
  • Hamdache Kamel
  Mathematical Methods in the Applied Sciences, Wiley, 2007, 31 (2), pp.123-151.
• The Korteweg-de Vries equation with multiplicative homogeneous noise
  
  • de Bouard Anne
  • Debussche Arnaud
  , 2007, pp.113-133.